Alright, so, since the definition of "indie" varies, and no time is set, I just thought I'd touch on artists that could be considered "indie" in one way or another.

1. Neutral Milk Hotel - If you've never heard In The Aeroplane Over The Sea, you're doing yourself a grave injustice.

2. The Murdocks - a indie/power-pop trio out of Texas. Their sound varies from hard rock to softer stuff, but definitely an indie gem. Franklin Morris, lead singer/guitarist, is a down to earth guy as well.

3. Bright Eyes - I don't know if you could consider these fellows indie anymore due to their popularity, but I think Oberst is a terrific songwrite. I'm Wide Awake It's Morning is my personal favorite, though his music touches on rock, acoustic-stuff, and even songs with electronic elements.

4. Regina Spektor - Again, she's signed to a major, but in terms of popularity I suppose she could still be considered indie. Personally, her lyrics are hit or miss for me, but singing-wise, I believe she is one of the best voices in modern music.

6. Cross Eyed Mary - A little-known band from Australia. They have songs with a blues influence and others with a strong rock influence. I personally love these guys and totally suggest you check them out. I've spoken with them and they were extremely down to earth.

7. Girl In A Coma - A trio of rock 'n' roll darlings, this is a band I enjoy immensely. Their newest album, Trio B.C., just came out earlier this month, but I enjoy their first album more. A STRONG reccomendation.

8. The Kills - I'm still quite new to The Kills, but I enjoy them quite a bit and would urge other indie fans to give 'em a listen. One track that's stuck in my head is "Tape Song".

9. Dave Smallen - Formerly of the band Street To Nowhere, Dave has gone out on his own as a solo artist, creating a style of music that varies from rock to country-like tracks. Definitely check him out! He's a terrific guy as well.

10. The Jesus and Mary Chain - I believe they got lost in the grunge shuffle of the 90's, but they're an excellent sort of band.

Lots of great bands are being mentioned, but I'm not exactly sure I'd call them indie. Maybe the OP could set some parameters. Do you mean the band releases its music on an independent label, or do you mean "indie" more as a style? Because I love Franz Ferdinand as much as many people seem to, but their latest release was on Sony Records. It doesn't get any less indie than that. Here are a few of my favorites:

I don't understand why a lot of these bands are on here personally, but I guess that the point of indie labels is to release music that the majority of people deem unlistenable, which is the way I categorize Jens Lekman and anything on Secretly Canadian. I realize though that some music is for almost everyone and some is for almost no one and it takes more courage to release the latter. Also Death Cab for Cutie is absolutely not an indie band. Just saying... anyway:

SpoonCold War KidsThe Go! TeamThe Beautiful GirlsBlitzen TrapperDr. DogWolf ParadeThe KillsThe Black Keysa lot of people signed to Sub Pop including (and I know some people won't count them but...) Flight of the Conchords